Block #840,738

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 12/5/2014, 9:01:46 AM · Difficulty 10.9742 · 6,003,793 confirmations

TWN

Bi-Twin Chain

Interleaved pairs of primes that differ by 2, forming twin prime pairs at each level.

Block Header

Block Hash

26a8cbf5ba1c1e2332aed1234139edb545ef1dc3d5070cd2d9601aed6033673c

View on Chainz ↗

Height

#840,738

Difficulty

10.974242

Transactions

Size

427 B

Version

Bits

0af967f4

Nonce

736,057,948

Timestamp

12/5/2014, 9:01:46 AM

Confirmations

6,003,793

Mined by

⛏️ P2SHAHkULawadwySPJdJkD2pMtbgtEPHU49wsM

Merkle Root

2e9d6b0d9cf9a7c271f1e35833d7700c7eaf34844759c7b6c6b46d6eda5ca232

Transactions (2)

Coinbasec7684e27cd3e0d…33cb1693faea06

1 in → 1 out8.3050 XPM110 B

AHkULawa…PHU49wsM

bdd3aebb53c51e…7c7eb8529c2437

1 in → 2 out0.0516 XPM226 B

AQXcSUAo…udNNpfwk AWEJp2mz…UTttM9Uk

Prime Chain Origin

This is the prime chain origin stored in the block header. It is a composite number (not prime itself) — it equals the first prime in the chain multiplied by a primorial. The origin anchors the entire chain to this specific block.

1.394 × 10⁹⁷(98-digit number)

13948803536792539347…08632456567509237759

Discovered Prime Numbers

Lower: 2^k × origin − 1 | Upper: 2^k × origin + 1

These are the actual prime numbers discovered by this block, computed using the verified Primecoin formula. Each number has been independently confirmed to pass the Fermat primality test. Use the FactorDB links to verify any number independently.

Level 0 — Twin Prime Pair (origin ± 1)

origin − 1

1.394 × 10⁹⁷(98-digit number)

13948803536792539347…08632456567509237759

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.394 × 10⁹⁷(98-digit number)

13948803536792539347…08632456567509237761

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: origin + 1 − origin − 1 = 2 (twin primes ✓)

Level 1 — Twin Prime Pair (2^1 × origin ± 1)

2^1 × origin − 1

2.789 × 10⁹⁷(98-digit number)

27897607073585078695…17264913135018475519

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.789 × 10⁹⁷(98-digit number)

27897607073585078695…17264913135018475521

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^1 × origin + 1 − 2^1 × origin − 1 = 2 (twin primes ✓)

Level 2 — Twin Prime Pair (2^2 × origin ± 1)

2^2 × origin − 1

5.579 × 10⁹⁷(98-digit number)

55795214147170157391…34529826270036951039

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

5.579 × 10⁹⁷(98-digit number)

55795214147170157391…34529826270036951041

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^2 × origin + 1 − 2^2 × origin − 1 = 2 (twin primes ✓)

Level 3 — Twin Prime Pair (2^3 × origin ± 1)

2^3 × origin − 1

1.115 × 10⁹⁸(99-digit number)

11159042829434031478…69059652540073902079

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.115 × 10⁹⁸(99-digit number)

11159042829434031478…69059652540073902081

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^3 × origin + 1 − 2^3 × origin − 1 = 2 (twin primes ✓)

Level 4 — Twin Prime Pair (2^4 × origin ± 1)

2^4 × origin − 1

2.231 × 10⁹⁸(99-digit number)

22318085658868062956…38119305080147804159

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

2.231 × 10⁹⁸(99-digit number)

22318085658868062956…38119305080147804161

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^4 × origin + 1 − 2^4 × origin − 1 = 2 (twin primes ✓)

Level 5 — Twin Prime Pair (2^5 × origin ± 1)

2^5 × origin − 1

4.463 × 10⁹⁸(99-digit number)

44636171317736125912…76238610160295608319

Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 11 consecutive prime numbers forming a Bi-Twin Chain. The prime chain origin — the large number shown above — anchors the chain and is divisible by a primorial (the product of small primes), cryptographically tying these prime numbers to this specific block.

★★★☆☆

Rarity

RareChain length 11

Approximately 1 in 1,000 blocks. Noteworthy discoveries.

How Primecoin's Proof-of-Work Constructs These Primes

Primecoin stores a value called the prime chain origin in each block. The miner found a large integer such that when divided by a primorial (the product of small primes: 2 × 3 × 5 × 7 × …), the result is the first prime in the chain. The origin is deliberately divisible by this primorial — that divisibility is part of the proof.

Prime Chain Origin = First Prime × Primorial (2·3·5·7·11·…)

Source: Primecoin prime.cpp — CheckPrimeProofOfWork()

This is why the origin has many small prime factors — those factors are the primorial divisor. The chain then extends from the first prime using the TWN formula:

TWN: twin pairs (p, p+2) where p = origin/primorial − 1 and p+2 = origin/primorial + 1

Cross-reference on Chainz Explorer

Block #840,738

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